Hello Adrian,
Not sure if this helps you. I also had problems finding items I had previously accessed and saved from Ancestry's "Historical Newspapers, Birth, Marriage, & Death Announcements, 1851-2003".
The database seems to have been removed, however, if I click on the saved source in my Ancestry tree, the following appears and I can click on the view record or view image buttons and they are still available to view

- Source citation for Historical Newspapers, Birth, Marriage, & Death Announcements, 1851-2003 screen capture
- Source citation for Historical Newspapers, Birth, Marriage, & Death Announcements, 1851-2003 screen capture.JPG (46.23 KiB) Viewed 1883 times

- Historical Newspapers, Birth, Marriage, & Death Announcements, 1851-2003 View Record Source screen capture.
- Historical Newspapers, Birth, Marriage, & Death Announcements, 1851-2003 View Record Source screen capture.JPG (162.98 KiB) Viewed 1883 times
The New York Times was definitely part of the collection.
The Source tab :
Source Information
Ancestry.com. Historical Newspapers, Birth, Marriage, & Death Announcements, 1851-2003 [database on-line]. Provo, UT, USA: Ancestry.com Operations Inc, 2006.
Original data:
The New York Times. New York, NY, USA: The New York Times, 1851-2001.
The Los Angeles Times. Los Angeles, CA, USA: The Los Angeles Times, 1881-1894.
The Boston Globe. Boston, MA, USA: The Boston Globe, 1872-1922.
The Chicago Defender. Chicago, IL, USA: The Chicago Defender, 1921-1975.
The Chicago Tribune. Chicago, IL, USA: The Chicago Tribune, 1850-1985.
The Hartford Courant. Hartford, CT, USA: The Hartford Courant, 1791-1942.
The Washington Post. Washington, D.C., USA: The Washington Post, 1877-1990.
The Atlanta Constitution. Atlanta, GA, USA: The Atlanta Constitution, 1868-1929.
Description
This database is a collection of birth, marriage, and death announcements from several major U.S. newspapers for a variety of years. Images of the original newspapers are included.
NB I can click on the bread crumbs of the item I saved :
Obituary > Los Angeles, California > 1918 > Los Angeles Times (1886-Current File), The
and manually change them to :
Obituary > New York, New York > [various years 1851-2003] > New York Times (1857-Current File)
and then scroll through the various images.

- Historical Newspapers, Birth, Marriage, & Death Announcements, 1851-2003 View Image after bread crumb change screen capture
- Historical Newspapers, Birth, Marriage, & Death Announcements, 1851-2003 View Image after bread crumb change screen capture.JPG (185.66 KiB) Viewed 1883 times
NB there are no images for 2007 ... Q. Is that the year of the record/image data or the year you accessed and saved the data?
I also note that there is a "Historical Newspapers Collection" which includes various separate newspaper databases
https://www.ancestry.com/search/categories/histnews/
I hope this helps you.
Geoff